Tomography generally refers to imaging by sections or sectioning, using any kind of penetrating wave. For example, X-ray computed micro-tomography (μ-CT), using the high fluxes from synchrotron sources, has evolved into a powerful imaging tool in the fields of physical and biological sciences due to its ability to image structure in three-dimensions (3-D) with high spatial resolution at macroscopic to sub-microscopic scales. With the development of increasingly complex structural materials that are finding increasing use in cutting-edge aerospace applications, such as fiber-reinforced ceramic composites and polymer-matrix composites, 3-D characterization of both structure and damage processes is essential, for it is the geometry, scale, and nature of these structures in all three dimensions that control their properties.
The last decade has witnessed the emergence of strong and tough ceramic-matrix composites, within which various design strategies are used on different spatial scales to overcome the brittleness that is inherent in materials that are able to survive extreme temperatures and chemically corrosive environments. Strong continuous fiber bundles (scale of 0.1 millimeters (mm) to 1 mm) are woven in custom-designed 3-D patterns, with individual bundles oriented in space so that they will follow the primary load paths expected in a given component to maximize its strength, and interlocked with one another to prevent catastrophic separation when damaged. Larger interstices between the fiber bundles may be partially filled with randomly-oriented fine reinforcing rods (scale of 1 micron (μm) to 10 μm), inhibiting local cracking under thermal shock. Coatings applied to individual fibers (scale of 0.1 μm to 1 μm) inhibit chemical reactions and ensure that the interfaces between the fibers and the matrix remain weak, allowing a ductile response through matrix cracking and frictional pullout of crack-bridging fibers. The remaining space between coated fibers, fiber bundles, and reinforcing rods is filled with a ceramic-matrix material, which itself may be a hybrid containing, for example, graphitic sheets that inhibit oxygen ingress (scale of 1 nanometer (nm) to 100 nm). Thus, like many natural materials, these new ceramic composites achieve robustness through complexity: their hierarchical, hybrid microstructure impedes the growth of local damage and prevents the large fatal cracks that are characteristic of brittle materials.
However, complexity in composition brings complexity in safe use. Most engineering structures, airframes, ships, buildings, etc., are designed to tolerate quite large cracks, which can be safely left monitored but unattended if they are less than a critical length, e.g., 10 mm or more in an airframe. Such cracks are large compared to the internal microstructural heterogeneity of a conventional material, which makes the prediction of their growth relatively easy; the effects of heterogeneity on crack growth tend to average out and therefore need not be included explicitly in engineering safety codes. For ceramic composites in ultrahigh-temperature applications, especially where corrosive species in the environment must be kept out of the material, relatively small cracks, on the order of the thickness of a fiber bundle (about 1 mm), can be unacceptable. These new ceramic materials thus violate the simplifying maxim of most traditional materials, that they be considered homogeneous on the scale at which damage becomes critical.
Exactly how micro-cracks are restrained by such tailored microstructure becomes the central question for the materials scientist who seeks to find the optimal composition or architecture and the design engineer who must predict the failure envelope. These questions raise many challenges, and the conditions of interest may be extreme. Observational methods based on direct imaging of the surface are complicated by high thermal noise. The properties (strength, etc.) of the composite's constituent materials and their interfaces are generally unknown at high temperature; they are also difficult to calibrate by independent tests, because the strength of different phases combined at nanometer and micron scales is not represented by tests on large specimens of the phase isolated as a monolithic material.